When an alien satellite causes all of Earth’s transmissions suddenly stop, a retired physicist must find a way to bring them back.

Understood, logically at some point other people on Earth either hear signal as well or become aware of the aliens. If they don't then the main character could just be going mad, only then it'll have the cliche moment when the audience are told - 'it was all in his head' which could be a weak twist.

I suggest you add a hint of irony to the mystery.

What if the physicist is also, unbeknown to him, part alien, and therefore is the only person on Earth that can understand the alien language. He is then perfectly qualified for being the only man on Earth who can stop them and the whole situation becomes imbued with mystery due to his strange connection with?the aliens.